Polytope of Type {2,4,14,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,14,4,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076475)
Rank : 6
Schlafli Type : {2,4,14,4,2}
Number of vertices, edges, etc : 2, 4, 28, 28, 4, 2
Order of s0s1s2s3s4s5 : 28
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,14,4,2}*896, {2,4,14,2,2}*896
4-fold quotients : {2,2,14,2,2}*448
7-fold quotients : {2,4,2,4,2}*256
8-fold quotients : {2,2,7,2,2}*224
14-fold quotients : {2,2,2,4,2}*128, {2,4,2,2,2}*128
28-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)
( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 87,101)( 88,102)
( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)
( 97,111)( 98,112)( 99,113)(100,114);;
s2 := ( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)( 10, 66)
( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 73)( 18, 79)
( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)( 26, 85)
( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31,101)( 32,107)( 33,106)( 34,105)
( 35,104)( 36,103)( 37,102)( 38,108)( 39,114)( 40,113)( 41,112)( 42,111)
( 43,110)( 44,109)( 45, 87)( 46, 93)( 47, 92)( 48, 91)( 49, 90)( 50, 89)
( 51, 88)( 52, 94)( 53,100)( 54, 99)( 55, 98)( 56, 97)( 57, 96)( 58, 95);;
s3 := ( 3, 4)( 5, 9)( 6, 8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)( 19, 23)
( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 53)( 32, 52)( 33, 58)( 34, 57)
( 35, 56)( 36, 55)( 37, 54)( 38, 46)( 39, 45)( 40, 51)( 41, 50)( 42, 49)
( 43, 48)( 44, 47)( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)
( 73, 74)( 75, 79)( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87,109)( 88,108)
( 89,114)( 90,113)( 91,112)( 92,111)( 93,110)( 94,102)( 95,101)( 96,107)
( 97,106)( 98,105)( 99,104)(100,103);;
s4 := ( 3, 31)( 4, 32)( 5, 33)( 6, 34)( 7, 35)( 8, 36)( 9, 37)( 10, 38)
( 11, 39)( 12, 40)( 13, 41)( 14, 42)( 15, 43)( 16, 44)( 17, 45)( 18, 46)
( 19, 47)( 20, 48)( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25, 53)( 26, 54)
( 27, 55)( 28, 56)( 29, 57)( 30, 58)( 59,101)( 60,102)( 61,103)( 62,104)
( 63,105)( 64,106)( 65,107)( 66,108)( 67,109)( 68,110)( 69,111)( 70,112)
( 71,113)( 72,114)( 73, 87)( 74, 88)( 75, 89)( 76, 90)( 77, 91)( 78, 92)
( 79, 93)( 80, 94)( 81, 95)( 82, 96)( 83, 97)( 84, 98)( 85, 99)( 86,100);;
s5 := (115,116);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(116)!(1,2);
s1 := Sym(116)!( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)
( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 87,101)
( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)
( 96,110)( 97,111)( 98,112)( 99,113)(100,114);
s2 := Sym(116)!( 3, 59)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)( 9, 60)
( 10, 66)( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 73)
( 18, 79)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31,101)( 32,107)( 33,106)
( 34,105)( 35,104)( 36,103)( 37,102)( 38,108)( 39,114)( 40,113)( 41,112)
( 42,111)( 43,110)( 44,109)( 45, 87)( 46, 93)( 47, 92)( 48, 91)( 49, 90)
( 50, 89)( 51, 88)( 52, 94)( 53,100)( 54, 99)( 55, 98)( 56, 97)( 57, 96)
( 58, 95);
s3 := Sym(116)!( 3, 4)( 5, 9)( 6, 8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)
( 19, 23)( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 53)( 32, 52)( 33, 58)
( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 46)( 39, 45)( 40, 51)( 41, 50)
( 42, 49)( 43, 48)( 44, 47)( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)
( 69, 71)( 73, 74)( 75, 79)( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87,109)
( 88,108)( 89,114)( 90,113)( 91,112)( 92,111)( 93,110)( 94,102)( 95,101)
( 96,107)( 97,106)( 98,105)( 99,104)(100,103);
s4 := Sym(116)!( 3, 31)( 4, 32)( 5, 33)( 6, 34)( 7, 35)( 8, 36)( 9, 37)
( 10, 38)( 11, 39)( 12, 40)( 13, 41)( 14, 42)( 15, 43)( 16, 44)( 17, 45)
( 18, 46)( 19, 47)( 20, 48)( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25, 53)
( 26, 54)( 27, 55)( 28, 56)( 29, 57)( 30, 58)( 59,101)( 60,102)( 61,103)
( 62,104)( 63,105)( 64,106)( 65,107)( 66,108)( 67,109)( 68,110)( 69,111)
( 70,112)( 71,113)( 72,114)( 73, 87)( 74, 88)( 75, 89)( 76, 90)( 77, 91)
( 78, 92)( 79, 93)( 80, 94)( 81, 95)( 82, 96)( 83, 97)( 84, 98)( 85, 99)
( 86,100);
s5 := Sym(116)!(115,116);
poly := sub<Sym(116)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope